In this section we present two examples that meet the conditions of
Definition REF . The first example stems from an exact
discretization of a continuous-time \((x,u)\) -flat system, and is flat
but not forward-flat. In fact, it allows not a single decomposition
as proposed in [1]}, and thus does not
meet the corresponding necessary condition for forward-flatness. Accordingly,
the test for forward-flatness stated in [2]}
fails in the first step. Hence, the example proves that the class
of forward-flat systems is a strict subset of the class of flat systems.
